Percentage increase when adding a specific amount

Question

Is it possible to calculate $X$ if $100$ has been added to $X$ as a result of a $234$% increase?

So, I want to calculate what I started with from the statement "up \$$100$ ($+234$%) in the past $6$ months."

Is there a general formula for this, perhaps?

Answer 1

If $X$ increases $100$%, it becomes $2X$. So, by similar logic, if $X$ is increased by $234$%, then it becomes $3.34X$. However, we also notice that $100$ is added to $X$ due to this increase, thus $3.34X=X+100$.

More generally, if $X$ is increased by $m$%, and this increases $X$ by $n$ amount, then this relationship can be describe by this formula $X(1+\frac{m}{100}) = X +n$.

Answer 2

If $X$ gets increased by $234\%$, then it becomes $X+2.34X=3.34X$. And if you add $100$ to $X$, you get $X+100$. So, $X+100=3.34X$. Can you take it form here?

Answer 3

HINT

Increasing $X$ by $234$ per cent is the same as multiplying it by 3.34.

So you have an equation $X+100=3.34X$.

Answer 4

An Increase of $234 \%$ is equal to $\$100$.

Meaning the original base quantity $X$ (which can also be viewed as $100 \% X$ is simply $\$ \frac {100}{234} (100) = \$ \frac{100}{2.34} \approx \$ 42.74$ to the nearest cent.

The simple rule of thumb is divide the percentage increase by $100$, get that value. Then take the dollar amount increase and divide by the value. That will give you the original amount.